The Admissions Process:

Is it possible to defer admission for one or two years? (Be aware that many schools will defer only for a compelling reason, and that funding offered with the original acceptance usually is not deferred and a new package may not be as strong as the original.)

Financial Aid:

What is the application process? What criteria is important?

What percentage of students holds fellowships or teaching/research assistantships? What is the likelihood of your being a recipient?

If one defers, what happens to funding that was offered with the original acceptance? Many schools prefer that you not defer.

Students:

What is the class size? Composition of the class in terms of age, race, gender, sexual orientation, and whatever else is important to you?

How competitive are students with each other? Attrition rate?

What student organizations exist?

Faculty:

What is the student/faculty ratio? How available are faculty to students?

How culturally diverse are the faculty? Do faculty members represent a variety of viewpoints toward the discipline?

Are the research interests of faculty similar to your own?

Facilities:

How extensive and available are the labs and other training facilities? Are specialized research facilities available?

Are there cooperative programs with other educational, cultural, and research institutions?

Employment Potential:

What career services support is provided for graduate students?

What kinds of positions do graduates hold? Where, geographically, do graduates find positions? (Are there graduates working in the geographic areas where you might locate, giving you potential contacts for advice on your own job search?)

This is by no means an exhaustive list. What other questions pertain to your particular situation?